Improved perturbative QCD study of the decay <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msubsup> <mml:mi>B</mml:mi> <mml:mi>c</mml:mi> <mml:mo>+</mml:mo> </mml:msubsup> <mml:mo stretchy="false">→</mml:mo> <mml:msu

We perform an improved perturbative QCD study of the decays <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msubsup> <a:mi>B</a:mi> <a:mi>c</a:mi> <a:mo>+</a:mo> </a:msubsup> <a:mo stretchy="false">→</a:mo> <a:msub> <a:mi>η</a:mi> <a:mi>c</a:mi> </a:msub> <a:msup> <a:mi>L</a:mi> <a:mo>+</a:mo> </a:msup> </a:math> , where <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"> <d:mi>L</d:mi> </d:math> denotes the light ground-state pseudoscalar, vector mesons and the corresponding <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"> <f:mi>p</f:mi> </f:math> -wave scalar, axial-vector, and tensor ones, and predict their branching ratios (BRs) associated with relative ratios at leading order in the strong coupling <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"> <h:msub> <h:mi>α</h:mi> <h:mi>s</h:mi> </h:msub> </h:math> . Our results <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"> <j:mrow> <j:mi>BR</j:mi> </j:mrow> <j:mo stretchy="false">(</j:mo> <j:msubsup> <j:mi>B</j:mi> <j:mi>c</j:mi> <j:mo>+</j:mo> </j:msubsup> <j:mo stretchy="false">→</j:mo> <j:msub> <j:mi>η</j:mi> <j:mi>c</j:mi> </j:msub> <j:msup> <j:mi>π</j:mi> <j:mo>+</j:mo> </j:msup> <j:mo stretchy="false">)</j:mo> <j:mo>=</j:mo> <j:mo stretchy="false">(</j:mo> <j:mn>2.0</j:mn> <j:msubsup> <j:mn>3</j:mn> <j:mrow> <j:mo>−</j:mo> <j:mn>0.41</j:mn> </j:mrow> <j:mrow> <j:mo>+</j:mo> <j:mn>0.53</j:mn> </j:mrow> </j:msubsup> <j:mo stretchy="false">)</j:mo> <j:mo>×</j:mo> <j:msup> <j:mn>10</j:mn> <j:mrow> <j:mo>−</j:mo> <j:mn>3</j:mn> </j:mrow> </j:msup> </j:math> and <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:mrow> <q:mi>BR</q:mi> </q:mrow> <q:mo stretchy="false">(</q:mo> <q:msubsup> <q:mi>B</q:mi> <q:mi>c</q:mi> <q:mo>+</q:mo> </q:msubsup> <q:mo stretchy="false">→</q:mo> <q:msub> <q:mi>η</q:mi> <q:mi>c</q:mi> </q:msub> <q:msup> <q:mi>π</q:mi> <q:mo>+</q:mo> </q:msup> <q:mo stretchy="false">)</q:mo> <q:mo>/</q:mo> <q:mrow> <q:mi>BR</q:mi> </q:mrow> <q:mo stretchy="false">(</q:mo> <q:msubsup> <q:mi>B</q:mi> <q:mi>c</q:mi> <q:mo>+</q:mo> </q:msubsup> <q:mo stretchy="false">→</q:mo> <q:mi>J</q:mi> <q:mo>/</q:mo> <q:mi>ψ</q:mi> <q:msup> <q:mi>π</q:mi> <q:mo>+</q:mo> </q:msup> <q:mo stretchy="false">)</q:mo> <q:mo>=</q:mo> <q:mn>1.7</q:mn> <q:msubsup> <q:mn>4</q:mn> <q:mrow> <q:mo>−</q:mo> <q:mn>0.50</q:mn> </q:mrow> <q:mrow> <q:mo>+</q:mo> <q:mn>0.66</q:mn> </q:mrow> </q:msubsup> </q:math> are consistent with several available predictions in different approaches within uncertainties. Inputting the measured <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"> <y:msub> <y:mi>η</y:mi> <y:mi>c</y:mi> </y:msub> <y:mo stretchy="false">→</y:mo> <y:mi>p</y:mi> <y:mover accent="true"> <y:mi>p</y:mi> <y:mo stretchy="false">¯</y:mo> </y:mover> </y:math> and <db:math xmlns:db="http://www.w3.org/1998/Math/MathML" display="inline"> <db:msub> <db:mi>η</db:mi> <db:mi>c</db:mi> </db:msub> <db:mo stretchy="false">→</db:mo> <db:msup> <db:mi>π</db:mi> <db:mo>+</db:mo> </db:msup> <db:msup> <db:mi>π</db:mi> <db:mo>−</db:mo> </db:msup> <db:mo stretchy="false">(</db:mo> <db:msup> <db:mi>π</db:mi> <db:mo>+</db:mo> </db:msup> <db:msup> <db:mi>π</db:mi> <db:mo>−</db:mo> </db:msup> <db:mo>,</db:mo> <db:msup> <db:mi>K</db:mi> <db:mo>+</db:mo> </db:msup> <db:msup> <db:mi>K</db:mi> <db:mo>−</db:mo> </db:msup> <db:mo>,</db:mo> <db:mi>p</db:mi> <db:mover accent="true"> <db:mi>p</db:mi> <db:mo stretchy="false">¯</db:mo> </db:mover> <db:mo stretchy="false">)</db:mo> </db:math> BRs with <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"> <kb:mi>p</kb:mi> </kb:math> here being a proton, we derive the multibody <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"> <mb:msubsup> <mb:mi>B</mb:mi> <mb:mi>c</mb:mi> <mb:mo>+</mb:mo> </mb:msubsup> <mb:mo stretchy="false">→</mb:mo> <mb:msub> <mb:mi>η</mb:mi> <mb:mi>c</mb:mi> </mb:msub> <mb:mo stretchy="false">(</mb:mo> <mb:mi>π</mb:mi> <mb:mo>,</mb:mo> <mb:mi>ρ</mb:mi> <mb:msup> <mb:mo stretchy="false">)</mb:mo> <mb:mo>+</mb:mo> </mb:msup> </mb:math> BRs through secondary decay chains via resonance <rb:math xmlns:rb="http://www.w3.org/1998/Math/MathML" display="inline"> <rb:msub> <rb:mi>η</rb:mi> <rb:mi>c</rb:mi> </rb:msub> </rb:math> under the narrow-width approximation, which might facilitate the (near-)future tests of <tb:math xmlns:tb="http://www.w3.org/1998/Math/MathML" display="inline"> <tb:msub> <tb:mi>B</tb:mi> <tb:mi>c</tb:mi> </tb:msub> <tb:mo stretchy="false">→</tb:mo> <tb:msub> <tb:mi>η</tb:mi> <tb:mi>c</tb:mi> </tb:msub> </tb:math> decays. Under the <wb:math xmlns:wb="http://www.w3.org/1998/Math/MathML" display="inline"> <wb:mi